Versality for canonical curves and complete intersections (Q1364369)

Let \(X\) be a smooth subvariety of projective space \(\mathbb{P}^r\). This paper is centered on answering the question when do the nearby hyperplane sections versally deform any given hyperplane section. We show that this property holds when \(X\) is a general canonical curve or complete intersection and \(r\) is small, and that in most other cases this property fails.